Preheat oven to 400 degrees F.
Dice the onion, slice the mushrooms, chop the parsley.
Butterfly the chicken breasts. Take one chicken breast and start to slowly slice into the side, horizontally (see post images for reference). As you start to cut into the side, pull up on the top half to help the knife cutting straight through the center and not accidentally out the bottom. Continue to slice through the center horizontally until almost to the other side - do not slice all the way through - and then open the chicken up flat. Do this with all of the breasts.
Pound out the chicken. Place one of the butterflied chicken breasts between 2 pieces of plastic wrap and pound it out gently to be an even flat piece about ¼ inch thick. Do this with all of the breasts.
Lay one of the pounded out breasts flat and season the side that is up with salt and pepper. Then layer the mozzarella at one end. Roll the chicken around the mozzarella and secure the flap with toothpicks (see post images for reference). Season the outside of the rolls with salt and pepper. Do this for all of the chicken breasts.
In a preheated large frying pan or skillet over medium high heat, drizzle about a 1-2 teaspoons of Extra Virgin Olive Oil (to coat the bottom). Sear the chicken rolls on all sides. Turn off the heat and transfer the chicken rolls to a sheet pan and bake in the preheated oven for 15 minutes, until the internal temperature reaches 165 degrees F.
While the chicken is baking, using the same pan used for searing the chicken, turn the heat back on to medium heat. Add another drizzle (1-2 teaspoons) of olive oil and then add the diced onion. Cook for about 3 minutes.
Add the mushrooms along with oregano, 1 teaspoon salt and ½ teaspoon ground pepper. Cook for about 8-10 minutes, until the mushrooms get browned and are cooked down to about half or more of the original size.
Next add the flour and stir to combine. Add the chicken broth/stock and stir until it cooks down and turns into a thick sauce. Finally add in half the parsley, reserving the rest for garnish.
When the chicken is done, plate each roll with a heaping scoop of the mushroom sauce right over top. Enjoy!!